How much can an inclusion of the number of iterations have on the training of an MLP?
If anything, you want the learning rate to decrease as the number of iterations increases.
When you're looking for a good spot and you're clueless, take large steps. When you've found a pretty good spot, take small steps, so you don't end up far away.
In other fields of machine learning, there are studies of how the learning rate should scale. For example, in traditional reinforcement learning methods, if $\alpha_i$ is the learning rate at step $i$, then we want to have the following two criteria, to make sure we get convergence to the optimal policy:

$\sum_{i=0}^{\infty} \alpha_i = \infty$. This makes sure that, no matter how bad our initial experience was, we can eventually forget it and replace it with better information.
$\sum_{i=0}^{\infty} \alpha_i^2 &lt; \infty$. This guarantees eventual convergence.

A typical choice here is $\alpha_i = \frac{1}{1+i}$, which fits both criteria.
I am unaware of similar criteria for MLPs, but if you're going to modify the step sizes, I would follow a similar approach. Make the step sizes decrease, but not too fast.